How do I randomize the movement of trees made with the sapling generator?
If you need the forest to look more realistic, you would need more animations! One animation for all the trees is simply not enough. 

My suggestions:


Add at least 3-4 different animations. 
Make trees swap their animations randomly (e.g. tree1 runs animation1 then animation3...)
Don't randomise the rotation because that would look fake (wind blows generally in one direction)
Also be careful with the different wind speed as if you overdo this you might get unrealistic results.
You can simulate the wind 'gust' by starting the animations on all trees (seed points) which are at a certain position (say in X) and delay the animations of the other trees based on their Y position.
To make this even more effective you can actually simulate the wind by creating a huge box or a sphere(s) and animating them, passing through the forest in a certain way. This would be a non-renderable object which would trigger the wind animations on your trees. This could be even further enhanced if you increase the wind speed based on the proximity of the tree to the sphere centre, for example.
Also don't forget that even if you nail the whole wind animation, if you only have one tree model (despite different scale/rotation), it just wont work. You need more variation, only then you can play with randomness.